SITE-C teams: Lesson 11

A model rocketship is fired vertically into the air and reaches a height of 3456 feet in 3 seconds. What is the maximum height that the model rocketship reaches? How many seconds will it be in the air?

The height of a model rocketship fired vertically into the air can be expressed by the mathematical formula h(x) = v x - 16 x^{2} where v is the initial velocity in feet per second and x is time measured in seconds. To answer the questions posed we must first find the initial velocity. Since the rocket reaches 3456 feet in 3 seconds then using the formula we have:

3456 = v (3) - 16 (3)^{ 2}

Solving for v we have that the initial velocity was 1200 ft./sec.

Turn on the **CASIO CFX-9850G** by pressing

Use the cursor arrows to highlight the GRAPH menu and press **EXE **or just press **5** when at the main menu screen.

In the Y1 slot enter 1200 X - 16 X^{2} and press **EXE** to store it in memory.

Press **SHIFT** **MENU** (SETUP), use the down cursor arrow to scroll down and highlight the Derivative line, press **F1** (ON) **EXIT**.

Press **SHIFT** and **F3** (V-Window) to set the parameters as follows:

Xmin = 0 Ymin = -2500 |
Xmax = 75.6 Ymax = 27900 |
Xscale = 5 Yscale = 2500 |

Press **EXIT** to return to the function list. Make sure that no other Y-slot is highlighted, i.e. selected for drawing. Press **F6** (DRAW) to see the graph.

Press **SHIFT** **F2** (ZOOM) **F1** (BOX). Use the cursor arrows to move the cross hairs to a desired location for the top left-hand corner of the box, for example x = 37.2 and y = 22996.774193, press **EXE** to mark this position. Use the cursor arrows to move the cross hairs to a desired location for the bottom right-hand corner of the box, for example x = 37.8 and y = 22016.129032, press **EXE**.

Press** SHIFT F1** (Trace) and use the right cursor arrow to approach the maximum y-value. This occurs at x = 37.5 and y = 22500. Note that dY/dX = 0. This indicates that the model rocketship reaches its maximum height in 37.5 seconds and that height is 22500 feet above the ground. Furthermore, the velocity of the rocketship when it reaches that maximum is 0 ft/sec.

Press **SHIFT F2** (ZOOM) **F6** ( |> ) **F1** (ORIG) to return to the original viewing window.

Press** SHIFT F5** (G-Solv) **F1** (Root) and use the right cursor arrow to find the second root at x = 75. This means that the rocketship was in the air for 75 seconds.

Press **EXIT** **MENU**.

Turn off the **CASIO CFX-9850G** by pressing